Mathematical Inferences Research Articles

Stress invariants and invariants of the failure envelope as a quadric surface: Their significances in the formulation of a rational failure criterion

When stress invariants up to the second order are employed to construct failure criterion for brittle materials, it involves three independent terms and therefore there are three coefficients to be determined. However, there are only two conditions available associated with the strengths under uniaxial tension and compression. Systematic examinations have given to the invariants of the failure envelope as a quadric surface according to analytic geometry. For the failure envelope to meet the basic assumptions, in particular, infinite strength under and only under hydrostatic compression, one of the coefficients can be eliminated based on rigorous mathematical inferences. As a result, it reproduces the Raghava-Caddell-Yeh criterion, which has never been rationally established before but is now in this paper. The failure envelope takes the form of circular paraboloid for brittle materials in general. The criterion degenerates to the von Mises criterion, giving a circular cylindrical failure envelope for ductile materials as a special case. It is as rational as the von Mises criterion in the sense that the assumptions made and the conditions available are logically sufficient for the complete establishment of the failure criterion without any ambiguity.

Examining 5th Grade Students' Learning on Surface Area Calculations with Realistic Mathematics Education Approach

The fact that the mathematics course is abstract, that it is not possible to associate it with daily life, and that it is impossible to concretize abstract expressions causes a prejudice against the this course and leads to a decrease in the academic achievements of students. It is seen that throughout history, various studies have been carried out taking this situation into consideration. A group of these studies is on realistic mathematics education. Realistic mathematics education is an approach that aims to concretize the abstract concepts of mathematics by relating them to real-life situations. The purpose is to make mathematics more understandable by concretizing it. In the study, the subject of calculating the surface area of prisms with the use of realistic mathematics education was taught, and the purpose of the study was to examine the effects of this application. The study group consisted of 20 5th grade students. While determining this group, maximum variety sampling strategy was preferred. In the study, action research, one of the qualitative research methods, was used, and the data were interpreted with the help of descriptive analysis and content analysis. The data collection tools in the study included semi-structured interview forms, video recordings, photos and activity sheets prepared by the students under the guidance of the researcher in accordance with the realistic mathematics education approach. When the findings were examined, it was seen that the students showed a positive development in the meaning and visualization processes; that they could reach mathematical inferences on their own; that they enjoyed the mathematics lesson; and that the realistic mathematics education approach gave positive results on learning. Based on these results, it was suggested that not only the application of the realistic mathematics education approach for different acquisitions but also the inclusion of these activities in the textbooks in accordance with the curriculum will result in improvements in favor of learning.

Cognitive correlates of math abilities in autism spectrum disorder.

The purpose of the current study was to investigate the contribution of different cognitive processes to specific math abilities in students with autism spectrum disorder (ASD) and typically developing (TD) students. The study involved a group of students with ASD without intellectual disabilities (n = 26) and a group with TD students (n = 52). The two groups aged from six to 20 years old and were matched for age, sex ratio and visuospatial reasoning. To assess math abilities, four math tasks were administered: arithmetic facts, mental calculation, mathematical inferences and math problem solving. Concerning cognitive processes, participants were tested on vocabulary, verbal working memory, visuospatial working memory, response inhibition and interference control. The group with ASD showed lower scores on all specific math measures than the TD group; cognitive processes differently contributed to diverse math abilities, and vocabulary and verbal working memory were stronger associated to specific math abilities in the group with ASD than in the TD group. The current results suggest that students with ASD had lower math abilities that are generalized to different math tasks. Implications for research and clinical assessment and intervention were discussed.

A comparative analysis of the fuzzy and intuitionistic fuzzy environment for group and individual equipment replacement Models in order to achieve the optimized results

The main goal of this research is to compare group and individual replacement models based on fuzzy replacement theory and intuitionistic fuzzy replacement theory. The capital costs are assumed to be triangular fuzzy numbers, triangular intuitionistic fuzzy numbers, and trapezoidal intuitionistic fuzzy numbers, respectively. As a result, interpreting the direct relationship between volatility and ambiguity is critical. It is difficult to predict when specific equipment will unexpectedly fail. This problem can be solved by calculating the probability of failure distribution. Furthermore, the failure is assumed to occur only at the end of period t. In this situation, two types of replacement policies are used. The first is the Individual Replacement Policy, which states that if an item fails, it will be replaced immediately. The Group Replacement Policy states that all items must be replaced after a certain time period, with the option of replacing any item before the optimal time. The dimensions of the prosecution are fuzzy, and they are then assessed using mathematical and logical procedures. The fuzzy assessment criteria of the replacement model are provided as a set of outcomes, whereas the intuitionistic fuzzy replacement model has many advantages. A methodological technique is used to determine quality measurements in which fuzzy costs or values are kept without being merged into crisp values, allowing us to draw mathematical inferences in an uncertain setting. A comparison conceptualise is created for each fuzzy number, and in an uncertain environment, a comparison study on group and individual replacement was also conducted.

Examining 6th Grade Students’ Learning of the Subject of Volume with GeoGebra Software Within the Framework of RME Approach

In the world where we always meet geometric constructions, it is a necessity to make sense of the objects belonging to these constructions. In this respect, this study aimed to examine the teaching of volume with the blending of the realistic mathematics education (RME) and GeoGebra. The study group consisted of 12 students attending lessons regularly. In the study, action research was used, and the data obtained were interpreted with descriptive and content analysis. The data collection tools used in the study included semi-structured interview forms, video records, audio records and activity sheets prepared by the researcher in accordance with the RME approach. When the findings were examined, it was concluded that the positive impressions occurring in the visualization and interpretation processes of the students allowed the students to write mathematical sentences as well as to interpret the outputs by making mathematical inferences.

A novel family of edge preserving anisotropic filters

In this article, new anisotropic image filters are introduced and their performances are compared with existing isotropic and anisotropic filters. The developed filters were examined according to their image noise removing performances in terms of standard image quality metrics, as well as the edge preserving properties of the filtered images. Mathematical inferences of anisotropic filters are made based on the minimization of the Polyakov action energy integral. New anisotropic metrics are found by means of Finsler metrics that minimize the corresponding integral. The new metrics perform filtering by updating the image with anisotropic Laplace-Beltrami flow. After filtering, it was observed that the introduced metrics perform well against other anisotropic metrics. It is also observed that the developed New Randers, New Normalized Miron, and New Metric filters preserve edges better than other filters, making it a plausible noise removal tool prior to edge detection in image processing. The source codes of proposed filters are publicly available at https://github.com/HAYDARKILIC.

“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic

Abstract In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks concerning the development of infinitary logic. I also stress the fact that the second axiomatization of set theory provided by Zermelo in 1930 involved the use of extremal axioms of a very specific sort.1

Analysis and optimization of a five-phase hybrid excitation flux switching machine based on the consistency and complementarity principle

In this study, the general optimal stator poles/rotor teeth (P/T) combination equation of the E-core hybrid excitation flux switching (HEFS) machines are introduced, and a new HEFS machine is proposed and optimized. Firstly, the influences of three different P/T combinations (10/18, 10/19, and 10/21) on the HEFS machines are investigated with two-dimensional (2D) finite element analyses (2D-FEA). Meanwhile, the consistency and complementarity principle of the armature windings is analyzed in detail to give reasonable explanations to the simulated results. The general optimal P/T combination equation of the E-core HEFS machines is deduced mathematically to provide an effective guidance on the selection of P/T combinations. The optimal P/T combination calculated by the general equation agrees with the simulated results which confirm the correctness of the mathematical inferences. Finally, the optimizations on the proposed HEFS machine are implemented to obtain higher output torque and better flux-regulation ratio characteristics based on which the cogging torque and torque ripple are reduced significantly.

Agent–cellular automata model for the dynamic fluctuation of EV traffic and charging demands based on machine learning algorithm

Electric vehicles (EV) comprise one of the foremost components of the smart grid and tightly link the power system with the road network. Spatial and temporal randomness in electric charging distribution will exert negative impacts on power grid dispatch. Existing research focuses mainly on mathematical inferences from statistical data, and the dynamic movement of an individual vehicle traveling in a traffic system is rarely taken into account. Machine learning algorithm can take the EV dynamic condition into consideration. Based on machine learning algorithm, this paper proposes a charging demand simulation method based on the Agent–cellular automata model to describe the changes in location and the state of charge of a moving EV. CRUISE software is used to analyze power consumption in different scenarios. Then, the Monte Carlo algorithm models the dynamic fluctuation of EV traffic and charging demands. Case studies are conducted on a typical composite system consisting of a 54-node distribution system and a 25-node traffic network, and the simulation results demonstrate the effectiveness of the proposed method.

Логический и математический вывод: синтаксис и семантика доказательства

The paper treats the relation between mathematical and logical inferences in mathematics and analyses an ontological approach for explaining the indispensability of the semantic content from mathematical proof. It was shown that such an approach entails serious metaphysical commitments, that is why it is concluded that the epistemological approach is preferable in explaining the nature of the difference between the formal and mathematical inferences.

The Method of Statistical Inferences for Figures Based on Feature Extraction and Uncertain Dynamics’ Prediction

One of the important tasks of mathematical statistics is statistical inference. With the appearance of big data, however, statistical inference faces new challenges, especially when people want to make inferences for figures, sounds and words, or for the mixture of such kinds of components. In this paper, by using the method of feature extraction and the method on the prediction of uncertain dynamics, we propose the method on mathematical inferences for figures, and something like that. We intend to provide some inspirations to extend the methods of statistical inference to the new fields, and hope the method can be further extended to the inferences for other kinds of data.

Mathematical model of LsrR-binding and derepression in Escherichia coli K12.

Quorum sensing (QS) enables bacterial communication and collective behavior in response to self-secreted signaling molecules. Unlocking its genetic regulation will provide insight towards understanding its influence on pathogenesis, formation of biofilms, and many other phenotypes. There are few datasets available that link QS-mediated gene expression to its regulatory components and even fewer mathematical models that incorporate known mechanistic detail. By integrating these data with annotated sequence information, mathematical inferences can be pieced together that shed light on regulatory structure. A first principles model, developed here for the E. coli QS system, builds on known mechanistic detail and is used to develop a working model of LuxS-regulated (Lsr) activity. That is, our model is meant to discriminate among hypothetical mechanisms governing lsr transcriptional regulation. Our simulations are in qualitative agreement with experimentally observed data. Importantly, our results point to the importance of transcriptional regulator, LsrR, cycling on genetic control. We also found several experimental observations in E. coli and homologous systems that were not explained by current mechanistic understanding. For example, by comparing simulations with reports of the integrating host factor in Aggrigatibacter actinomycetemcomitans, we conclude that additional transcriptional components are likely involved. An iterative process of simulation and experiment, therefore, is needed to inform new experiments and incorporate new model detail, the benefit of which will more rapidly validate mechanistic understanding.

Space-borne Passive Microwave Remote Sensing of Soil Moisture: A Review

Soil moisture (SM) plays an important role in groundwater recharge, runoff, air moisture, atmospheric temperature, land degradation, geo-chemical process, surface and sub-surface biota including agriculture, etc. Several studies have reported comparable results of space-borne passive microwaves remote sensing of surface (2 to 5 cm) SM using relationship between volumetric SM and brightness temperature, dielectric constant, polarimetry, roughness parameter, mathematical inferences, etc. However, reported success studies are very site-, image -, overpass time-, model- and situation specific and insufficient to reach at global conclusions. Therefore, reported methods, techniques and algorithms should thoroughly be tested in different biophysical environments to assess applicability in SM retrievals using microwave data captured at different frequencies, polarization, angle, time, etc. Keywords: Calibrations, dielectric properties, enhancements, frequency, models, passive microwave, polarimetry, radiometry, remote sensing.

Mathematical Rigor, Proof Gap and the Validity of Mathematical Inference

Mathematical rigor is commonly formulated by mathematicians and philosophers using the notion of proof gap: a mathematical proof is rigorous when there is no gap in the mathematical reasoning of the proof. Any philosophical approach to mathematical rigor along this line requires then an account of what a proof gap is. However, the notion of proof gap makes sense only relatively to a given conception of valid mathematical reasoning, i.e., to a given conception of the validity of mathematical inference. A proof gap can in particular be conceived as a failure in drawing a valid mathematical inference. The aim of this paper is to discuss two possible views of the validity of math­ematical inference with respect to their capacity to yield a plausible account of the intuitive notion(s) of proof gap present in mathematical practice. The first view is the one provided by the contemporary standards of mathematical rigor: a mathematical inference is valid if and only if its conclusion can be formally derived from its premises. We will argue that this conception does not lead to a plausible account of the intuitive notion(s) of proof gap. The second view is based on a new account of the validity of inference proposed by Prawitz: an inference is valid if and only if it consists in an operation that provides a ground for its conclusion given (previously obtained) grounds for its premises. We will first specify Prawitz's account to mathematical inference and we will then argue that the resulting ground-based account is able to capture various intuitive notions of proof gap as different types of failure in drawing valid mathematical inferences. We conclude that the ground-based account ap­pears of particular interest for the philosophy of mathematical practice, and we finally raise several challenges facing a full development of a ground-based account of the notions of mathematical rigor, proof gap and the validity of mathematical inference.

A Mathematical Calculation Model Using Biomarkers to Quantitatively Determine the Relative Source Proportion of Mixed Oils

Abstract: It is difficult to identify the source(s) of mixed oils from multiple source rocks, and in particular the relative contribution of each source rock. Artificial mixing experiments using typical crude oils and ratios of different biomarkers show that the relative contribution changes are non‐linear when two oils with different concentrations of biomarkers mix with each other. This may result in an incorrect conclusion if ratios of biomarkers and a simple binary linear equation are used to calculate the contribution proportion of each end‐member to the mixed oil. The changes of biomarker ratios with the mixing proportion of end‐member oils in the trinal mixing model are more complex than in the binary mixing model. When four or more oils mix, the contribution proportion of each end‐member oil to the mixed oil cannot be calculated using biomarker ratios and a simple formula. Artificial mixing experiments on typical oils reveal that the absolute concentrations of biomarkers in the mixed oil cause a linear change with mixing proportion of each end‐member. Mathematical inferences verify such linear changes. Some of the mathematical calculation methods using the absolute concentrations or ratios of biomarkers to quantitatively determine the proportion of each end‐member in the mixed oils are deduced from the results of artificial experiments and by theoretical inference. Ratio of two biomarker compounds changes as a hyperbola with the mixing proportion in the binary mixing model, as a hyperboloid in the trinal mixing model, and as a hypersurface when mixing more than three end‐members. The mixing proportion of each end‐member can be quantitatively determined with these mathematical models, using the absolute concentrations and the ratios of biomarkers. The mathematical calculation model is more economical, convenient, accurate and reliable than conventional artificial mixing methods.

Linguistic Invention and Semantic Warrant Production: Elementary Teachers’ Interpretation of Graphs

In this qualitative study of mathematical discourse between elementary teachers, we examined linguistic invention and semantic warrant production as participants made successive attempts to communicate mathematical ideas. Linguistic invention is a creative practice of describing mathematics in terms of personal experience. We introduce semantic warrant production, which emerged as part of our analysis of substantial arguments produced by teachers learning mathematics. Participants engaged in linguistic invention and semantic warrant production to convince themselves and others of the validity of their mathematical inferences about a graph of rate of change versus time. Personal experiences that are taken-as-shared in a learning community can support accurate mathematical inference if connections between conventional language, common experiences, and mathematical representations are made explicit by learners.

The history of mathematics: a brief course

Preface to the Second Edition. PART 1: THE WORLD OF MATHEMATICS AND THE MATHEMATICS OF THE WORLD. Chapter 1. The Origin and Prehistory of Mathematics. Chapter 2. Mathematical Cultures I. Chapter 3. Mathematical Cultures II. Chapter 4. Women Mathematicians. PART 2: NUMBERS. Chapter 5. Counting. Chapter 6. Calculation. Chapter 7. Ancient Number Theory. Chapter 8. Numbers and Number Theory in Modren Mathematics. PART 3: COLOR PLATES. PART 4: SPACE. Chapter 9. Measurement. Chapter 10. Euclidean Geometry. Chapter 11. Post-Euclidean Geometry. Chapter 12. Modern Geometries. PART 5: ALGEBRA. Chapter 13. Prolems Leading to Algebra. Chapter 14. Equations and Methods. Chapter 15. Modern Algebra. PART 6: ANALYSIS. Chapter 16. The Calculus. Chapter 17. Real and Complex Aanlysis. PART 7: MATHEMATICAL INFERENCES. Chapter 18. Probability and Statistics. Chapter 19. Logic and Set Theory. Literature. Subject Index. Name Index.

Quality control in histopathology and diagnostic cytology.

The need for quality control in diagnostic histopathology and cytology is analysed together with a discussion of previously reported experience in this field. The philosophical and mathematical inferences of this type of exercise are debated also in relationship to personally observed experiences in respect of uterine cervical cytology and histology. The desirability of methods of monitoring of diagnostic quality and of obtaining quality improvement are emphasized and suggestions made regarding the techniques most suited to these objectives.

Statistical inference: fiducial and structural vs. likelihood

The mathematical model assumptions, justifying fiducial, structural or likelihood inferences, are discussed. In this connection is clarified, that the known paradoxes with fiducial or structural can be avoided by a careful distinction between functional and distributional models.

Some Mathematical and Computational Contributions to Underwater Sound Propagation

This study of underwater acoustic propagation seeks, first, to determine just what can be known concerning the medium (velocity as a function of position and time, conditions of bottom and surface, etc.), so that the mathematical inferences therefrom can be realistic; second, to apply to this purpose the most powerful modern mathematical tools; third, to implement the results by efficient methods of numerical computation. Starting with the standard wave equation and energy-flux vector, specializations are made for traveling waves of high frequency, in which the energy flux is along the bi-characteristics (rays). To the latter are applied Hamiltonian methods: perturbation theory, integral, invariants and statistical information theory, etc. The wave is also treated directly by modern mathematical methods. The numerical methodology takes advantage of these analytic results, and is further simplified by avoiding levels of detail inconsistent with the levels of knowledge. Relatively simple and powerful computer programs are developed when sound speed depends on depth only; they are extended by perturbation methods to a more general case, including small but not negligible horizontal gradients. The statistical effects of fluctuations of actual from average profiles are examined. [Work was supported by the Naval Ordnance System Command.]